{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,11,11]],"date-time":"2026-11-11T15:06:21Z","timestamp":1794409581939,"version":"4.9.0"},"reference-count":33,"publisher":"Wiley","issue":"17","license":[{"start":{"date-parts":[[2010,4,20]],"date-time":"2010-04-20T00:00:00Z","timestamp":1271721600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Statistics in Medicine"],"published-print":{"date-parts":[[2010,7,30]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In repeated measures settings, modeling the correlation pattern of the data can be immensely important for proper analyses. Accurate inference requires proper choice of the correlation model. Optimal efficiency of the estimation procedure demands a parsimonious parameterization of the correlation structure, with sufficient sensitivity to detect the range of correlation patterns that may occur. Many repeated measures settings have within\u2010subject correlation decreasing exponentially in time or space. Among the variety of correlation patterns available for this context, the continuous\u2010time first\u2010order autoregressive correlation structure, denoted AR(1), sees the most utilization. Despite its wide use, the AR(1) structure often poorly gauges within\u2010subject correlations that decay at a slower or faster rate than required by the AR(1) model. To address this deficiency we propose a two\u2010parameter generalization of the continuous\u2010time AR(1) model, termed the linear exponent autoregressive (LEAR) correlation structure, which accommodates much slower and much faster decay patterns. Special cases of the LEAR family include the AR(1), compound symmetry, and first\u2010order moving average correlation structures. Excellent analytic, numerical, and statistical properties help make the LEAR structure a valuable addition to the suite of parsimonious correlation models for repeated measures data. Both medical imaging data concerning neonate neurological development and longitudinal data concerning diet and hypertension [DASH (Dietary Approaches to Stop Hypertension) study] exemplify the utility of the LEAR correlation structure. Copyright \u00a9 2010 John Wiley &amp; Sons, Ltd.<\/jats:p>","DOI":"10.1002\/sim.3928","type":"journal-article","created":{"date-parts":[[2010,4,20]],"date-time":"2010-04-20T17:07:23Z","timestamp":1271783243000},"page":"1825-1838","source":"Crossref","is-referenced-by-count":40,"title":["A linear exponent AR(1) family of correlation structures"],"prefix":"10.1002","volume":"29","author":[{"given":"Sean L.","family":"Simpson","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lloyd J.","family":"Edwards","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Keith E.","family":"Muller","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Pranab K.","family":"Sen","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Martin A.","family":"Styner","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2010,4,20]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1002\/sim.2827"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1002\/sim.4780070108"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.2307\/2531727"},{"key":"e_1_2_1_5_2","first-page":"989","article-title":"A note on the covariance structure of a continuous\u2010time ARMA process","volume":"10","author":"Tsai H","year":"2000","journal-title":"Statistica Sinica"},{"key":"e_1_2_1_6_2","first-page":"156","article-title":"Improving the quality of forecasting using generalized AR models: an application to statistical quality control","volume":"5","author":"Peiris MS","year":"2003","journal-title":"Statistical Methods"},{"key":"e_1_2_1_7_2","volume-title":"Statistical Methods for Spatial Data Analysis","author":"Schabenberger O","year":"2005"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1198\/016214506000001347"},{"key":"e_1_2_1_9_2","volume-title":"Statistics for Spatial Data","author":"Cressie NAC","year":"1991"},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.2307\/2532340"},{"key":"e_1_2_1_11_2","unstructured":"MurraySC.Linear models with generalized AR(1) covariance structure for irregularly\u2010timed data. Unpublished Dissertation University of North Carolina at Chapel Hill 1990."},{"key":"e_1_2_1_12_2","doi-asserted-by":"publisher","DOI":"10.1002\/sim.4780142004"},{"key":"e_1_2_1_13_2","doi-asserted-by":"publisher","DOI":"10.1002\/sim.4780141302"},{"key":"e_1_2_1_14_2","doi-asserted-by":"publisher","DOI":"10.1148\/radiol.2353040716"},{"key":"e_1_2_1_15_2","doi-asserted-by":"publisher","DOI":"10.3174\/ajnr.A0751"},{"key":"e_1_2_1_16_2","doi-asserted-by":"publisher","DOI":"10.1056\/NEJM199704173361601"},{"key":"e_1_2_1_17_2","doi-asserted-by":"publisher","DOI":"10.1161\/01.HYP.34.3.472"},{"key":"e_1_2_1_18_2","doi-asserted-by":"publisher","DOI":"10.1198\/016214507000000095"},{"key":"e_1_2_1_19_2","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198522065.001.0001","volume-title":"Time Series: A Biostatistical Introduction","author":"Diggle PJ","year":"1990"},{"key":"e_1_2_1_20_2","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/87.2.425"},{"key":"e_1_2_1_21_2","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/90.1.43"},{"key":"e_1_2_1_22_2","doi-asserted-by":"publisher","DOI":"10.1080\/03610910701649598"},{"key":"e_1_2_1_23_2","doi-asserted-by":"publisher","DOI":"10.2307\/2530695"},{"key":"e_1_2_1_24_2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1111\/j.2517-6161.1977.tb01600.x","article-title":"Maximum likelihood for incomplete data via the EM algorithm","volume":"39","author":"Dempster AP","year":"1977","journal-title":"Journal of the Royal Statistical Society, Series B"},{"key":"e_1_2_1_25_2","doi-asserted-by":"publisher","DOI":"10.2307\/2290128"},{"key":"e_1_2_1_26_2","volume-title":"SAS\/IML, Version 9","author":"SAS Institute","year":"2002"},{"key":"e_1_2_1_27_2","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.1974.1100705"},{"key":"e_1_2_1_28_2","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176344136"},{"key":"e_1_2_1_29_2","doi-asserted-by":"publisher","DOI":"10.1198\/jasa.2009.0116"},{"key":"e_1_2_1_30_2","doi-asserted-by":"publisher","DOI":"10.1002\/0471728438"},{"key":"e_1_2_1_31_2","doi-asserted-by":"publisher","DOI":"10.1002\/sim.3429"},{"key":"e_1_2_1_32_2","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1987.10478472"},{"key":"e_1_2_1_33_2","doi-asserted-by":"publisher","DOI":"10.1002\/0470052147"},{"key":"e_1_2_1_34_2","volume-title":"Matrix Analysis for Statistics","author":"Schott JR","year":"1997"}],"container-title":["Statistics in Medicine"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fsim.3928","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/sim.3928","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,2,20]],"date-time":"2025-02-20T02:52:18Z","timestamp":1740019938000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/sim.3928"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,4,20]]},"references-count":33,"journal-issue":{"issue":"17","published-print":{"date-parts":[[2010,7,30]]}},"alternative-id":["10.1002\/sim.3928"],"URL":"https:\/\/doi.org\/10.1002\/sim.3928","archive":["Portico"],"relation":{},"ISSN":["0277-6715","1097-0258"],"issn-type":[{"value":"0277-6715","type":"print"},{"value":"1097-0258","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,4,20]]}}}